The emissivity of tungsten is 0.350. A tungsten sphere with radiu...

Question

The emissivity of tungsten is 0.350. A tungsten sphere with radius 1.50 cm is suspended within a large evacuated enclosure whose walls are at 290.0 K. What power input is required to maintain the sphere at 3000.0 K if heat conduction along the supports is ignored?

Accepted Answer

Welcome back everybody. We are looking at a chromium cube that is inside some sort of vacuum container. Now we are told that the thickness of this cube is 0.12 m. We are told that chromium has an emissivity of 0.28. And we are told that the chromium cube is used for heating right now. The temperature of the walls of its casing are 283 kelvin and we are wishing to maintain a temperature of the cube to be 811. Now we are asked to find what is the power supply needed to maintain this temperature. Well, in order to maintain the same temperature, that means the power supply needed is equal to the radiation rate of the chromium cube. And we have a formula for the radiation rate it is uh, the emissivity times the Stefan bolts. Hman constant times the area of the chromium cube, times the desired temperature of the cube. To the power of four minus the temperature of the surroundings. To the power of four. Well, we have all the information we need. So let's just go ahead and plug it into this formula. Emissivity is given by 0.28. The Stefan bolts man constant is 5.67 times 10 to the negative eight watts per meter squared times seven to the fourth. Uh and then we have times the area while the area of the chromium crew has given, sorry Cube is given by six times the side length. Or sorry, the thickness of its 0. square times the desired temperature of 811 kelvin to the power four minus the temperature of the surroundings. To the power of four, which, when you plug all of this into your calculator, you get that. Our desired radiation rate equal to our power supply needed is 5.85 watts, corresponding to our answer. Choice of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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